Definition

A power of ten is 10 raised to a whole number.

For example, 10¹ = 10; 10² = 100; 10³ = 1000 and so on.

A power of a ten has one followed by as many zeros as the power.

For example, 10² is equal to one followed by two zeros, i.e., 100.

Rule

When a decimal number is multiplied by a power of ten, the product is found by moving the decimal point to the right that many places as the power of ten.

For example, in 3.45 10², the product is obtained by moving the decimal point two places to the right, i.e., 3.452 10² = 345.2

Problem 1

Multiply 4.569 10²

Solution

Step 1:

4.569 10²

Here the power of ten is two or the number of zeros in its value 100 is 2.

Step 2:

So the decimal point in 4.569 is moved 2 places to the right and the product is obtained as shown below.

4.569 10² = 4.569 100 = 456.9

Problem 2

Multiply 17.3426 10³

Solution

Step 1:

17.3426 10³

Here the power of ten is three or the number of zeros in its value 1000 is 3.

Step 2:

So the decimal point in 17.3426 is moved 3 places to the right and the product is obtained as shown below.

17.3426 10³ = 17.3426 1000 = 17342.6

Introduction

Decimal multiplication is done in a similar way as whole number multiplication.

Rules for Decimal Multiplication

• First we multiply the decimal numbers as if they were whole numbers by ignoring the decimal points.
• Here the decimal points are not lined up vertically as in addition and subtraction. Here the digits are lined up to the right.
• The number of digits after the decimal point in both the numbers are counted and added.
• In the final product, a decimal point is placed before that many digits from the right.

Problem 1

Multiply 13.4 0.35

Solution

Step 1:

13.4 0.35

We line up the digits and not the decimal points

We now multiply the numbers by ignoring the decimal points and assuming as if they were whole numbers.

Step 2:

13.4 has one decimal place. 0.35 has two decimal places. So the product of these numbers has three decimal places.

Problem – 2

Multiply 16.5 0.27

Solution

Step 1:

16.5 0.27

We line up the digits and not the decimal points

We now multiply the numbers by ignoring the decimal points and assuming as if they were whole numbers.

Step 2:

16.5 has one decimal place. 0.27 has two decimal places. So the product of these numbers has three decimal places.

Decimal multiplication is like whole number multiplication.

Rules for Multiplication of a Decimal by a Whole Number

• In the multiplication of a decimal number by a whole number, we first multiply the numbers by ignoring the decimal point.
• We then put the decimal point before as many places in the product as there are in the decimal number.

Problem 1

Multiply 0.13 25

Solution

Step 1:

0.13 25

Multiplying without decimal point 13 25 = 325

Step 2:

The number of decimal places in 0.13 is two

The number of decimal places in 25 is zero

So the product has two decimal places, i.e., 3.25

Problem – 2

Multiply 0.24 18

Solution

Step 1:

0.24 18

Multiplying without decimal point 24 18 = 432

Step 2:

The number of decimal places in 0.24 is two

The number of decimal places in 18 is zero

So the product has two decimal places, i.e., 4.32

Decimal multiplication is similar to whole number multiplication.

Rules for Decimal Multiplication

• First we multiply the decimal numbers as if they were whole numbers by ignoring the decimal points.
• The number of digits after the decimal point in both the numbers are counted and added.
• In the final product, a decimal point is placed before that many digits from the right.

Problem 1

Multiply 0.07 2.3

Solution

Step 1:

0.07 2.3

Multiplying without decimal points 7 23 = 161

Step 2:

The number of decimal places in 0.07 is 2

The number of decimal places in 2.3 is 1

Step 3:

So the product has three decimal places i.e.,0.07 2.3 = 0.161

Problem 2

Multiply 0.06 3.1

Solution

Step 1:

0.06 3.1

Multiplying without decimals 6 31 = 186

Step 2:

The decimal places in 0.06 is 2

The decimal places in 3.1 is 1

Step 3:

So the product has three decimal places i.e., 0.06 3.1 = 0.186

This tutorial provides comprehensive coverage of multiplication and division of decimals based on Common Core CCSS and State Standards and its prerequisites. Students can navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular needs. This simple tutorial uses appropriate examples to help you understand multiplication and division of decimals in a general and quick way.

Audience

This tutorial has been prepared for beginners to help them understand the basics of multiplication and division of decimals. After completing this tutorial, you will find yourself at a moderate level of expertise in multiplication and division of decimals, from where you can advance further.

Prerequisites

Before proceeding with this tutorial, you need a basic knowledge of elementary math concepts such number sense, multiplication, division, place values of whole numbers, place value chart, definition of decimal numbers and so on.